Reconsidering the role of disembedding in multiplicative concepts: Extending theory from the process of developing a quantitative measure

ABSTRACT

Multiplicative reasoning as articulated through scheme theory suggests that students improve the sophistication of their reasoning as they are able to coordinate additional levels of units, often described through students’ use of schemes and operation at particular multiplicative concepts. Theoretical descriptions of the second and third multiplicative concepts (MC2 and MC3) suggest that students use disembedding as part of schemes for coordinating three levels of units. The present article proposes a refined conceptualization of disembedding multiplicative contexts based on analysis of quantitative pilot data from the development of a measure for multiplicative reasoning. Results suggest that students at MC2 are more likely to engage in schemes involving disembedding when the disembedding involves units of 1. Disembedding involving composite units is more probabilistically aligned with students at MC3. Implications for theory and research are provided.

KEYWORDS:

• Disembedding
• multiplication & division
• multiplicative reasoning
• scheme theory